Some extremely amenable groups
| dc.creator | Giordano, Thierry | |
| dc.creator | Pestov, Vladimir | |
| dc.date | 2001-09-19 | |
| dc.date | 2001-10-27 | |
| dc.date.accessioned | 2026-07-07T08:26:58Z | |
| dc.date.available | 2026-07-07T08:26:58Z | |
| dc.description | A topological group $G$ is extremely amenable if every continuous action of $G$ on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of a Lebesgue space with a non-atomic measure is extremely amenable with the weak topology but not with the uniform one. Strengthening a de la Harpe's result, we show that a von Neumann algebra is approximately finite-dimensional if and only if its unitary group with the strong topology is the product of an extremely amenable group with a compact group. | |
| dc.description | 7 pages, English with abridged French version | |
| dc.identifier | https://arxiv.org/abs/math/0109138 | |
| dc.identifier | http://arxiv.org/abs/math/0109138 | |
| dc.identifier | C.r. Acad. Sci. Paris, Ser. I 334 (2002), No. 4, 273-278. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137122 | |
| dc.subject | Group Theory | |
| dc.subject | Dynamical Systems | |
| dc.subject | Operator Algebras | |
| dc.subject | 43A07; 37A15; 46L10 | |
| dc.title | Some extremely amenable groups | |
| dc.type | text |